The order, signed on Friday in Washington, temporarily banned refugees from around the world from entering the US, blocked Syrian refugees indefinitely and placed severe restrictions on immigration from seven predominantly Muslim countries — Iraq, Syria, Iran, Yemen, Sudan, Libya and Somalia.

Members of religious minorities from those countries, however, will be granted immigration priority.

Political reaction to the order ranged across the partisan divide.

On Friday, Democratic Senate minority leader Chuck Schumer said: “Tears are running down the cheeks of the Statue of Liberty tonight as a grand tradition of America, welcoming immigrants, that has existed since America was founded, has been stomped upon.”

Republican House speaker Paul Ryan countered: “Our number one responsibility is to protect the homeland. I support the refugee resettlement program, but… President Trump is right to make sure we are doing everything possible to know exactly who is entering our country.”

As Trump spoke by phone to the leaders of Japan, France, Germany and Russia on Saturday, international reaction to the ban was largely negative.

British Prime Minister Theresa May, however, ducked a series of questions at a press conference with the Turkish prime minister, 24 hours after meeting Trump in Washington.

Asked several times what she thought of Trump’s order, she finally replied: “The US is responsible for its policy on refugees.”

The Iranian foreign ministry said in a statement the executive order was an “open affront against the Muslim world and the Iranian nation”. Iran will “take appropriate consular, legal and political measures”, it said.

In New York City, two Iraqi refugees who arrived on separate flights were detained at John F Kennedy airport.

One, Hameed Khalid Darweesh, had worked in Iraq for the US government for 10 years.

The other, Haider Sameer Abdulkhaleq Alshawi, was coming to the US to join his wife who had worked for a US contractor, according to a report in the New York Times.

An immigration organisation in New York City said it was dispatching an expert to the airport to try to establish how many people were being held in limbo as border agents began preventing Muslims in particular from entering the country.

Thanu Yakupitiyage, a spokeswoman for the New York Immigration Coalition (NYIC), told the Guardian: “This is absolutely dehumanising, I am livid, it’s outrageous. We are sending someone to JFK airport to speak to customs and border control about this, people are in a state of shock.”